Question

A person travels 120 km at the speed of 60 km/hr, 30 km at the speed of 30 km/hr and 90 km at the
speed of 90 km/hr. Find the average speed of the person.​

Answer 1

Answer:

Total distance to be covered = 120 Km

Overall average speed for the entire journey = 60 Km/hr

Overall average speed = Total distance / total time taken

60 Km/hr = 120Km / total time

therefore, the total time required = 120 Km / 60 Km/hr = 2 hrs

For the first part of the journey,

30 Km was covered at an average speed of 30 Km/hr,

Time taken = Distance / speed = 30 Km / 30 Km/hr = 1 hr

For the second part of the journey,

Distance left = 120 Km - 30 Km = 90 Km

Time left = Total time - Time taken by first part of the journey

Time left = 2 hrs - 1 hr = 1hr

The average speed required for the second part of the journey to achieve an overall average speed of 60 Km = Distance left / Time left = 90 Km / 1 hr = 90 Km/hr

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Answer 2

The average speed of the person is 60 km/h.

Given,

Covered 120 km at 60 km/h

Covered 30 km at 30 km/h

Covered 90 km at 90 km/h

To Find,

The average speed of the person

Solution,

The formula for average speed is given as follows -

Average Speed = $\frac{Total Distance}{Total Time}$

Total distance = d₁ + d₂ + d₃

Total distance = 120 + 30 + 90

Total distance = 240 km

Total Time = t₁ + t₂ + t₃

t₁ = d₁/v₁

t₁ = $\frac{120}{60}$ = 2 hours

t₂ = d₂/v₂

t₂ = $\frac{30}{30}$ = 1 hour

t₃ = d₃/v₃

t₃ = $\frac{90}{90}$ = 1 hour

Total Time = 2 + 1 + 1

Total Time = 4 hours

Average Speed = $\frac{240}{4}$

Average Speed = 60 km/h

Thus, the average speed is 60 km/h.

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